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As long as the ground is dry and not alot of loose dirt and rock, 80% street/20% dirt tires will go anywhere you want on an average dual sport bike. I don't know about the differences in specs for dirt/street rims
As for gearing, I run a separate set for trail and street.
Trail gears can idle and creep up the slow trails and give a more torquier feel to the engine.
Road gears keep your bikes RPMs down at higher speeds and keeps the vibrations down as well.
I run trail gears around town with no problems, but I stay away from long higher speed runs on the highway.